Archive / Investment Adviser (Level 1) / Evaluating the Financial Position of Clients

nism-series-xa-cagr-compounded-annual-growth-rate-formula[ INVESTMENT ADVISER (LEVEL 1) ]

An investment of ₹1,00,000 grows to ₹2,50,000 over a holding period of exactly 6 years. What is the Compounded Annual Growth Rate (CAGR)?

[ A ]25.00% p.a. (Simple arithmetic average: 150% gain / 6 years)

[ B ]150.00% (Absolute holding period return)

[ C ]10.00% p.a.

[ D ]16.50% p.a. [ (FV / PV)^(1/n) - 1 = (2.50)^(1/6) - 1 ][ CORRECT ]

Takeaway

Option D is correct: 16.50% p.a. [ (FV / PV)^(1/n) - 1 = (2.50)^(1/6) - 1 ]

Derivation

Total growth factor = ₹2,50,000 / ₹1,00,000 = 2.50. CAGR annualizes this using the compounding exponent 1/n = 1/6 = 0.16667: CAGR = (2.50)^0.16667 − 1 ≈ 1.16499 − 1 = 16.50% p.a. This differs sharply from simply dividing the total 150% gain by 6 years to get 25%, because that linear method ignores that each year's growth compounds on top of the prior year's already-grown base rather than growing off the original principal every time. CAGR is the standard way to compare investments held for different periods on an apples-to-apples annualized basis, which is exactly why exams test it against the tempting but wrong simple-average shortcut.

Why the others fail

A — 25.00% p.a. (Simple arithmetic average: 150% gain / 6 years)

Divides the total 150% gain evenly across 6 years without compounding, which overstates the true annual growth rate versus the correctly compounded 16.50%.

B — 150.00% (Absolute holding period return)

States the total holding-period return of 150% without annualizing it at all, which is not comparable to a per-annum CAGR figure.

C — 10.00% p.a.

Understates the compounded annual growth needed to turn ₹1,00,000 into ₹2,50,000 over 6 years; the correctly compounded figure is 16.50%, not this lower one.